One mild surprise, given the space’s intimacy and its warm acoustics, is that Page and Davis were fitted with wireless microphones for the show. Paul Peterson, the Globe’s sound guru, said that won’t be the practice for most productions in the White (which is likely to host more straight plays than musicals).

But to be sure that lyrics could be heard over the music — and that an actor’s vocals wouldn’t drop out when she turned her back to part of the audience (which, in a theater-in-the-round, can hardly be avoided) — miking was necessary, Peterson said.

The amplification wasn’t obtrusive, although occasionally there was that vague ventriloquist’s effect of Page’s singing voice seeming to issue from somewhere toward the ceiling.

More notable was the fact there’s even a place to put musicians in this space. The White’s stage is about the same size as the Carter’s, but it’s fully trapped; for “I Do! I Do!,” the two-piece ensemble was perched in a cozy “pit” below one corner of the set.

The sophisticated lighting grid also seemed to produce richer harmonies of illumination (under Chris Rynne’s design) than were evident before.

“I Do! I Do” writer-lyricist Jones, who rewrote part of the first act for Page and Davis’ revival of the work, was on hand for the Globe opening. In a post-performance Q&A, he said it was the first time he had seen the musical — which won a Tony for Robert Preston opposite Mary Martin in its Broadway debut — staged in the round.

“It has a sacrificial feel,” he cracked, perhaps alluding to those bloody affairs at the Roman Colosseum.

“I Do! I Do!” doesn’t go for nearly that level of hostility, though there’s some epic quarreling in the gently comic piece, based on Jan de Hartog’s “The Fourposter,” about 50 years in the marriage of Michael and Agnes.

Jones admitted that he and Schmidt thought the idea of a “Fourposter” musical adaptation was “a really terrible idea” when they were first approached about it some 45 years ago.

It’s hard to imagine that any production featuring the eminently engaging and funny Page and Davis could be a terrible idea, but it’s hard to avoid feeling that for all their talents, the piece itself is out of tune with the times. Its ideas about gender roles are dated and clichéd, and the characters don’t feel drawn beyond prototypes.

Still, this is just the first rough go-round for Page and Davis with the piece, and it does have the enduring song “My Cup Runneth Over” tucked in its tuxedo pocket. With just a snag here and there, the White Theatre has tossed “I Do! I Do!” a pretty nice bouquet.